This paper illustrates how a deterministic approximation of a stochastic process
can be usefully applied to analyse the dynamics of many simple simulation models. To
demonstrate the type of results that can be obtained using this approximation, we present two
illustrative examples which are meant to serve as methodological references for researchers
exploring this area. Finally, we prove some convergence results for simulations of a family
of evolutionary games, namely, intra-population imitation models in n-player games with
arbitrary payoffs.